Library Subscription: Guest
Begell Digital Portal Begell Digital Library eBooks Journals References & Proceedings Research Collections
Journal of Porous Media

Impact factor: 1.035

ISSN Print: 1091-028X
ISSN Online: 1934-0508

Volumes:
Volume 20, 2017 Volume 19, 2016 Volume 18, 2015 Volume 17, 2014 Volume 16, 2013 Volume 15, 2012 Volume 14, 2011 Volume 13, 2010 Volume 12, 2009 Volume 11, 2008 Volume 10, 2007 Volume 9, 2006 Volume 8, 2005 Volume 7, 2004 Volume 6, 2003 Volume 5, 2002 Volume 4, 2001 Volume 3, 2000 Volume 2, 1999 Volume 1, 1998

Journal of Porous Media

DOI: 10.1615/JPorMedia.v17.i9.20
pages 763-784

WELL-POSEDNESS AND NUMERICAL SOLUTION OF A NONLINEAR VOLTERRA PARTIAL INTEGRO-DIFFERENTIAL EQUATION MODELING A SWELLING POROUS MATERIAL

Keith J. Wojciechowski
Department of Mathematics, Statistics, and Computer Science, University of Wisconsin−Stout, 202D Jarvis Hall Science Wing, 41010th Avenue East, Menomonie, WI54751-0790, USA
Jinhai Chen
Department of Mathematical and Statistical Sciences, University of Colorado−Denver, Campus Box 170, PO Box 173364, Denver, CO 80217-3364, USA
Lynn Schreyer-Bennethum
Department of Mathematical and Statistical Sciences, University of Colorado−Denver, Campus Box 170, PO Box 173364, Denver, CO 80217-3364, USA
Kristian Sandberg
Computational Solutions, Inc., 1800 30th St. Suite 210B, Boulder, CO 80301-1088, USA

ABSTRACT

We mathematically analyze an initial-boundary value problem that involves a nonlinear Volterra partial integro-differential equation derived using hybrid mixture theory and used to model swelling porous materials where the application is an immersed, porous cylindrical material imbibing fluid through its exterior boundary. The model is written as an initial-boundary value problem and we establish well-posedness and numerically solve it using a novel approach to constructing pseudospectral differentiation matrices in a polar geometry. Numerical results are obtained and interpretations are provided for a small variety of diffusion and permeability coefficients and parameters to simulate the model's behavior and to demonstrate its viability as a model for swelling porous materials exhibiting viscoelastic behavior.